arXiv research

Study shows volume and genus unrelated for hyperbolic fibred knots.

Countries tend to diversify their exports by entering products that are related to their current exports. Yet this average behavior is not representative of every diversification path. In this paper, we introduce a method to identify periods when countries enter unrelated products. We analyze the economic diversificati…

Study on fibered knots in 3-manifolds, proving unrelated volume and genus.

New model improves inference on asset market durations.

Develops a contrastive framework for data-efficient multimodal learning.

Training on mixed distributions improves test performance even when components are unrelated.

In this paper we show that two seemingly unrelated problems in economics, the hypothesis of integrability and the hypothesis of additive separability are linked by the absence of curvature of connections on webs naturally associated with each problem.

Quasi-orthonormal encoding reduces high dimensionality for categorical data.

We present an axiomatic modification of quaternionic quantum mechanics with a possible-worlds semantics capable of predicting essential "nonquantum" features of an observable universe model - the dimensionality and topology of spacetime, the existence, the signature and a specific form of a metric on it, and certain na…

Reviews six finance topics, including 'radical complexity'.

We find maximal representatives within equivalence classes of metric spheres. For Ahlfors regular spheres these are uniquely characterized by satisfying the seemingly unrelated notions of Sobolev-to-Lipschitz property, or volume rigidity. We also apply our construction to solutions of the Plateau problem in metric spac…

Recently, a number of statistical problems have found an unexpected solution by inspecting them through a "modal point of view". These include classical tasks such as clustering or regression. This has led to a renewed interest in estimation and inference for the mode. This paper offers an extensive survey of the tradi…

New method for rolling bodies on inclined planes, with applications to rescue operations.

We present a novel technique based on deep learning and set theory which yields exceptional classification and prediction results. Having access to a sufficiently large amount of labelled training data, our methodology is capable of predicting the labels of the test data almost always even if the training data is entir…

TQFT signatures linked to trace fields of knots.

We introduce a new class of quantum enhancements we call biquandle brackets, which are customized skein invariants for biquandle colored links.Quantum enhancements of biquandle counting invariants form a class of knot and link invariants that includes biquandle cocycle invariants and skein invariants such as the HOMFLY…

DERWENT learns paths for distant transfer learning via deep random walk.

Accurate goodness-of-fit tests for the extreme tails of empirical distributions is a very important issue, relevant in many contexts, including geophysics, insurance, and finance. We have derived exact asymptotic results for a generalization of the large-sample Kolmogorov-Smirnov test, well suited to testing these extr…

We propose a general-purpose approach to discovering active learning (AL) strategies from data. These strategies are transferable from one domain to another and can be used in conjunction with many machine learning models. To this end, we formalize the annotation process as a Markov decision process, design universal s…

We show how binary classification methods developed to work on i.i.d. data can be used for solving statistical problems that are seemingly unrelated to classification and concern highly-dependent time series. Specifically, the problems of time-series clustering, homogeneity testing and the three-sample problem are addr…

Boosts barely robust learners to be more adversarially robust.

We present a new approach for detecting related crime series, by unsupervised learning of the latent feature embeddings from narratives of crime record via the Gaussian-Bernoulli Restricted Boltzmann Machines (RBM). This is a drastically different approach from prior work on crime analysis, which typically considers on…

Correlated component analysis as proposed by Dmochowski et al. (2012) is a tool for investigating brain process similarity in the responses to multiple views of a given stimulus. Correlated components are identified under the assumption that the involved spatial networks are identical. Here we propose a hierarchical pr…

Many complex systems exhibit extreme events far more often than expected for a normal distribution. This work examines how self-similar bursts of activity across several orders of magnitude can emerge from first principles in systems that adapt to information. Surprising connections are found between two apparently unr…

Neural recordings are nonstationary time series, i.e. their properties typically change over time. Identifying specific changes, e.g. those induced by a learning task, can shed light on the underlying neural processes. However, such changes of interest are often masked by strong unrelated changes, which can be of physi…

GRASP removes spurious correlations in fine-tuned models, improving task performance and reducing bias.

To compare entities of differing types and structural components, the artificial neural network paradigm was used to cross-compare structural components between heterogeneous documents. Trainable weighted structural components were input into machine-learned activation functions of the neurons. The model was used for m…

Mind wandering (MW) is a ubiquitous phenomenon which reflects a shift in attention from task-related to task-unrelated thoughts. There is a need for intelligent interfaces that can reorient attention when MW is detected due to its detrimental effects on performance and productivity. In this paper, we propose a deep lea…

A generalized cusp $C$ is diffeomorphic to $[0,\infty)$ times a closed Euclidean manifold. Geometrically $C$ is the quotient of a properly convex domain by a lattice, $Γ$, in one of a family of affine groups $G(ψ)$, parameterized by a point $ψ$ in the (dual closed) Weyl chamber for $SL(n+1,\mathbb{R})$, and $Γ$ determi…

We consider how the problem of determining normal forms for a specific class of nonholonomic systems leads to various interesting and concrete bridges between two apparently unrelated themes. Various ideas that traditionally pertain to the field of algebraic geometry emerge here organically in an attempt to elucidate t…

Which song will Smith listen to next? Which restaurant will Alice go to tomorrow? Which product will John click next? These applications have in common the prediction of user trajectories that are in a constant state of flux over a hidden network (e.g. website links, geographic location). What users are doing now may b…

Study finds stocks with higher cyber risk scores outperform others, indicating a market-wide cyber risk premium.

Counterexamples show deconfounder fails to control multi-cause confounding.

We discuss in this article a property of action of groups by isometries called "well displacing". An action is said to be well displacing, if the displacement function is equivalent to the the displacement function for the action on the Cayley graph. We relate this property with the fact that orbit maps are quasi-isome…

Novel framework for quantifying data distribution values.

The sequence $(x_n)_{n\in\mathbb N} = (2,5,15,51,187,\dots)$ given by the rule $x_n=(2^n+1)(2^{n-1}+1)/3$ appears in several seemingly unrelated areas of mathematics. For example, $x_n$ is the density of a language of words of length $n$ with four different letters. It is also the cardinality of the quotient of $(\math…

Investment strategies derived from commodity futures curves exploit dynamics in price movements.

Two case studies reveal hidden biases and confounders in machine learning models of biomedical data.

We establish a connection between two previously unrelated topics: a particular discrete version of conformal geometry for triangulated surfaces, and the geometry of ideal polyhedra in hyperbolic three-space. Two triangulated surfaces are considered discretely conformally equivalent if the edge lengths are related by s…

Unified theory linking node embeddings and graph representations.

In this work we investigate on the concept of "restraining bolt", envisioned in Science Fiction. Specifically we introduce a novel problem in AI. We have two distinct sets of features extracted from the world, one by the agent and one by the authority imposing restraining specifications (the "restraining bolt"). The tw…

Powerful generative models, particularly in Natural Language Modelling, are commonly trained by maximizing a variational lower bound on the data log likelihood. These models often suffer from poor use of their latent variable, with ad-hoc annealing factors used to encourage retention of information in the latent variab…

We show that many Lorentzian manifolds of dimension >2 do not admit a spacelike codimension-one foliation, and that almost every manifold of dimension >2 which admits a Lorentzian metric at all admits one which satisfies the dominant energy condition and the timelike convergence condition. These two seemingly unrelated…

This paper diagnoses factor-model pricing errors using a new method.

Characterizes fractional Dehn twist coefficient and proves slice-Bennequin inequality.

The application of deep learning (DL) models to the decoding of cognitive states from whole-brain functional Magnetic Resonance Imaging (fMRI) data is often hindered by the small sample size and high dimensionality of these datasets. Especially, in clinical settings, where patient data are scarce. In this work, we demo…

This paper addresses two seemingly unrelated problems, (a) What is the entropy and energy accounting in the Maxwell Demon problem? and (b) How can the efficiency of markets be measured? Here we show, in a simple model for the Maxwell Demon, the entropy of the universe increases by an amount eta=0.839995520 in going fro…

Poly-view contrastive learning improves image representation learning.